On “Gauge Renormalization” in Classical Electrodynamics

Abstract

In this paper we pay attention to the inconsistency in the derivation of the symmetric electromagnetic energy-momentum tensor for a system of charged particles from its canonical form, when the homogeneous Maxwell equations are applied to the symmetrizing gauge transformation, while the non-homogeneous Maxwell equations are used to obtain the motional equation. Applying the appropriate non-homogeneous Maxwell equation to both operations, we have revealed an additional symmetric term in the tensor, named as "compensating term". Analyzing the structure of this "compensating term", we suggested a method of "gauge renormalization, which allows transforming the divergent terms of classical electrodynamics (infinite self-force, self-energy and self-momentum) to converging integrals. The motional equation obtained for a non-radiating charged particle does not contain its self-force, and the mass parameter includes the sum of mechanical and electromagnetic masses. The motional equation for a radiating particle also contains the sum of mechanical and electromagnetic masses, and does not yield any "runaway solutions". It has been shown that the energy flux in a free electromagnetic field is guided by the Poynting vector, whereas the energy flux in a bound EM field is described by the generalized Umov vector, defined in the paper. The problem of "Poincare stresses" is also examined. It has been shown that the presence of the "compensating term" in the electromagnetic energy-momentum tensor allows a solution of the "4/3 problem", where the total observable mass of the electron is completely determined by the Poincare stresses and hence the conventional relativistic relationship between the energy and momentum is recovered.